To find the value of f1 given that f4 = 22 and the general sequence formulas fn = 1 and fn = 3, we first analyze the formulas. Based on the question, we can assume that fn represents a sequence that is built from previous values in some manner. The notations suggest a recursive relationship, … Read more
To solve for y in the system of equations given: 1. x + 3y = 6 2. 2x + 7y = 10 We can use either substitution or elimination method. Here, we will use the substitution method: First, let’s solve the first equation for x: x = 6 – 3y Now, substitute this expression for … Read more
To express the vertical stretch of the function y = x by a factor of 6, you need to multiply the output (y-value) of the function by 6. This means that for every value of x, the corresponding value of y will be increased by a factor of 6. The original function can be represented … Read more
A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This means that for any rational number r, it can be represented in the form: r = a/b Here, a is an … Read more
To convert the quadratic function from its standard form, y = x2 + 4x + 7, into vertex form, you need to complete the square. The vertex form of a quadratic function is given by: y = a(x – h)2 + k, where (h, k) is the vertex of the parabola. Here are the steps … Read more
Finding the Vertex of the Function To find the vertex of the quadratic function f(x) = x² + 12x, we can use the vertex formula or complete the square. The vertex form of a quadratic function is given by: f(x) = a(x – h)² + k where (h, k) is the vertex. We can also … Read more
To solve the inequality 4x + 12 < 16 + 8x, we need to isolate x on one side. Here’s how we can do it step by step: Start with the original inequality: 4x + 12 < 16 + 8x To get all the x terms on one side and constant terms on the other … Read more
To reflect a function across the x-axis, you need to transform the function by multiplying it by -1. This changes the sign of all the output values for the function. Given the function: f(x) = 508x The reflection across the x-axis can be represented as: g(x) = -f(x) Substituting in the original function: g(x) = … Read more
To solve the problem, we need to understand the relationship between the tangent line, the radius of the circle, and the measures of angles and arcs in a circle. In this scenario, line EF is tangent to circle G at point A. By the properties of circles, we know that a tangent line at a … Read more
To determine whether f(1) is a function for the given expression f(x) = 8 – 2×2, we first need to evaluate f(1). 1. **Substituting x with 1**: We start by replacing x in the function with 1: f(1) = 8 – 2(1)2 2. **Calculating**: Now, we perform the calculations step by step: (1)2 = 1 … Read more